LMFDB - Embedded newform 1849.2.a.n.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$14.7643393337$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} - 15 x^{16} + 106 x^{15} + 47 x^{14} - 897 x^{13} + 364 x^{12} + 3855 x^{11} + \cdots - 27 $ x^18 - 5x^17 - 15x^16 + 106x^15 + 47x^14 - 897x^13 + 364x^12 + 3855x^11 - 3223x^10 - 8851x^9 + 9909x^8 + 10400x^7 - 14483x^6 - 5118x^5 + 9945x^4 - 27x^3 - 2493x^2 + 513*x - 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$-1.70036$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.70036 q^{2} +1.15587 q^{3} +0.891224 q^{4} -1.76341 q^{5} +1.96539 q^{6} +0.594565 q^{7} -1.88532 q^{8} -1.66397 q^{9} +O(q^{10})$	\(q+1.70036 q^{2} +1.15587 q^{3} +0.891224 q^{4} -1.76341 q^{5} +1.96539 q^{6} +0.594565 q^{7} -1.88532 q^{8} -1.66397 q^{9} -2.99843 q^{10} -4.34581 q^{11} +1.03014 q^{12} +3.24267 q^{13} +1.01098 q^{14} -2.03827 q^{15} -4.98817 q^{16} -5.54154 q^{17} -2.82935 q^{18} +2.71801 q^{19} -1.57159 q^{20} +0.687239 q^{21} -7.38944 q^{22} +5.29682 q^{23} -2.17918 q^{24} -1.89039 q^{25} +5.51371 q^{26} -5.39093 q^{27} +0.529891 q^{28} -9.86102 q^{29} -3.46578 q^{30} +3.73006 q^{31} -4.71104 q^{32} -5.02318 q^{33} -9.42261 q^{34} -1.04846 q^{35} -1.48297 q^{36} +1.34602 q^{37} +4.62159 q^{38} +3.74810 q^{39} +3.32458 q^{40} -11.2155 q^{41} +1.16855 q^{42} -3.87309 q^{44} +2.93426 q^{45} +9.00650 q^{46} +4.08771 q^{47} -5.76566 q^{48} -6.64649 q^{49} -3.21435 q^{50} -6.40528 q^{51} +2.88995 q^{52} -2.41097 q^{53} -9.16652 q^{54} +7.66343 q^{55} -1.12095 q^{56} +3.14166 q^{57} -16.7673 q^{58} -0.735135 q^{59} -1.81655 q^{60} +5.11518 q^{61} +6.34245 q^{62} -0.989339 q^{63} +1.96587 q^{64} -5.71815 q^{65} -8.54121 q^{66} -3.84908 q^{67} -4.93875 q^{68} +6.12242 q^{69} -1.78276 q^{70} -3.83751 q^{71} +3.13711 q^{72} -7.45576 q^{73} +2.28873 q^{74} -2.18505 q^{75} +2.42235 q^{76} -2.58387 q^{77} +6.37312 q^{78} +13.3934 q^{79} +8.79617 q^{80} -1.23929 q^{81} -19.0703 q^{82} +7.79301 q^{83} +0.612483 q^{84} +9.77199 q^{85} -11.3980 q^{87} +8.19324 q^{88} +4.50944 q^{89} +4.98929 q^{90} +1.92798 q^{91} +4.72065 q^{92} +4.31146 q^{93} +6.95057 q^{94} -4.79295 q^{95} -5.44534 q^{96} +0.184960 q^{97} -11.3014 q^{98} +7.23130 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) $ 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} - 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} - 25 q^{18} - 31 q^{19} - 25 q^{20} - 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} - 27 q^{26} - 23 q^{27} - 20 q^{28} - 37 q^{29} + 17 q^{30} - 12 q^{31} - 39 q^{32} - 38 q^{33} - 14 q^{34} + 16 q^{35} + 47 q^{36} + 19 q^{37} + 56 q^{38} - 46 q^{39} + 6 q^{40} - 7 q^{41} + q^{42} + 7 q^{44} - 23 q^{45} + 47 q^{46} - q^{47} - 15 q^{48} - 6 q^{49} + 3 q^{50} - 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} - 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} - 28 q^{61} - 33 q^{62} - 26 q^{63} + 10 q^{64} - 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} - 7 q^{69} + 34 q^{70} - 86 q^{71} + 2 q^{72} + 27 q^{73} - 79 q^{74} - 31 q^{75} - 59 q^{76} - 43 q^{77} + 91 q^{78} + 17 q^{79} - 8 q^{80} - 10 q^{81} - 13 q^{82} - 12 q^{83} - 32 q^{84} - 28 q^{85} - 43 q^{87} + 23 q^{88} - 51 q^{89} + 10 q^{90} + 20 q^{91} + 18 q^{92} + 30 q^{93} + 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} + 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 - 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 - 25 * q^18 - 31 * q^19 - 25 * q^20 - 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 - 27 * q^26 - 23 * q^27 - 20 * q^28 - 37 * q^29 + 17 * q^30 - 12 * q^31 - 39 * q^32 - 38 * q^33 - 14 * q^34 + 16 * q^35 + 47 * q^36 + 19 * q^37 + 56 * q^38 - 46 * q^39 + 6 * q^40 - 7 * q^41 + q^42 + 7 * q^44 - 23 * q^45 + 47 * q^46 - q^47 - 15 * q^48 - 6 * q^49 + 3 * q^50 - 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 - 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 - 28 * q^61 - 33 * q^62 - 26 * q^63 + 10 * q^64 - 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 - 7 * q^69 + 34 * q^70 - 86 * q^71 + 2 * q^72 + 27 * q^73 - 79 * q^74 - 31 * q^75 - 59 * q^76 - 43 * q^77 + 91 * q^78 + 17 * q^79 - 8 * q^80 - 10 * q^81 - 13 * q^82 - 12 * q^83 - 32 * q^84 - 28 * q^85 - 43 * q^87 + 23 * q^88 - 51 * q^89 + 10 * q^90 + 20 * q^91 + 18 * q^92 + 30 * q^93 + 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 + 5 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.70036	1.20234	0.601168	−	0.799123i	$-0.294702\pi$
$2$	1.70036	1.20234	0.601168	+	0.799123i	$0.294702\pi$
$3$	1.15587	0.667340	0.333670	−	0.942690i	$-0.391713\pi$
$3$	1.15587	0.667340	0.333670	+	0.942690i	$0.391713\pi$
$4$	0.891224	0.445612
$5$	−1.76341	−0.788620	−0.394310	−	0.918978i	$-0.629016\pi$
$5$	−1.76341	−0.788620	−0.394310	+	0.918978i	$0.629016\pi$
$6$	1.96539	0.802367
$7$	0.594565	0.224725	0.112362	−	0.993667i	$-0.464158\pi$
$7$	0.594565	0.224725	0.112362	+	0.993667i	$0.464158\pi$
$8$	−1.88532	−0.666561
$9$	−1.66397	−0.554657
$10$	−2.99843	−0.948186
$11$	−4.34581	−1.31031	−0.655155	−	0.755494i	$-0.727397\pi$
$11$	−4.34581	−1.31031	−0.655155	+	0.755494i	$0.727397\pi$
$12$	1.03014	0.297375
$13$	3.24267	0.899355	0.449678	−	0.893191i	$-0.351539\pi$
$13$	3.24267	0.899355	0.449678	+	0.893191i	$0.351539\pi$
$14$	1.01098	0.270194
$15$	−2.03827	−0.526278
$16$	−4.98817	−1.24704
$17$	−5.54154	−1.34402	−0.672010	−	0.740542i	$-0.734569\pi$
$17$	−5.54154	−1.34402	−0.672010	+	0.740542i	$0.734569\pi$
$18$	−2.82935	−0.666884
$19$	2.71801	0.623554	0.311777	−	0.950155i	$-0.399076\pi$
$19$	2.71801	0.623554	0.311777	+	0.950155i	$0.399076\pi$
$20$	−1.57159	−0.351418
$21$	0.687239	0.149968
$22$	−7.38944	−1.57543
$23$	5.29682	1.10446	0.552232	−	0.833691i	$-0.313776\pi$
$23$	5.29682	1.10446	0.552232	+	0.833691i	$0.313776\pi$
$24$	−2.17918	−0.444823
$25$	−1.89039	−0.378079
$26$	5.51371	1.08133
$27$	−5.39093	−1.03749
$28$	0.529891	0.100140
$29$	−9.86102	−1.83115	−0.915573	−	0.402152i	$-0.868262\pi$
$29$	−9.86102	−1.83115	−0.915573	+	0.402152i	$0.868262\pi$
$30$	−3.46578	−0.632763
$31$	3.73006	0.669939	0.334970	−	0.942229i	$-0.391274\pi$
$31$	3.73006	0.669939	0.334970	+	0.942229i	$0.391274\pi$
$32$	−4.71104	−0.832803
$33$	−5.02318	−0.874423
$34$	−9.42261	−1.61596
$35$	−1.04846	−0.177222
$36$	−1.48297	−0.247162
$37$	1.34602	0.221285	0.110643	−	0.993860i	$-0.464709\pi$
$37$	1.34602	0.221285	0.110643	+	0.993860i	$0.464709\pi$
$38$	4.62159	0.749721
$39$	3.74810	0.600176
$40$	3.32458	0.525663
$41$	−11.2155	−1.75156	−0.875781	−	0.482710i	$-0.839653\pi$
$41$	−11.2155	−1.75156	−0.875781	+	0.482710i	$0.839653\pi$
$42$	1.16855	0.180312
$43$	0	0
$43$	0	0
$44$	−3.87309	−0.583890
$45$	2.93426	0.437413
$46$	9.00650	1.32794
$47$	4.08771	0.596253	0.298127	−	0.954526i	$-0.403638\pi$
$47$	4.08771	0.596253	0.298127	+	0.954526i	$0.403638\pi$
$48$	−5.76566	−0.832202
$49$	−6.64649	−0.949499
$50$	−3.21435	−0.454578
$51$	−6.40528	−0.896919
$52$	2.88995	0.400763
$53$	−2.41097	−0.331172	−0.165586	−	0.986195i	$-0.552952\pi$
$53$	−2.41097	−0.331172	−0.165586	+	0.986195i	$0.552952\pi$
$54$	−9.16652	−1.24741
$55$	7.66343	1.03334
$56$	−1.12095	−0.149793
$57$	3.14166	0.416123
$58$	−16.7673	−2.20165
$59$	−0.735135	−0.0957064	−0.0478532	−	0.998854i	$-0.515238\pi$
$59$	−0.735135	−0.0957064	−0.0478532	+	0.998854i	$0.515238\pi$
$60$	−1.81655	−0.234516
$61$	5.11518	0.654932	0.327466	−	0.944863i	$-0.393805\pi$
$61$	5.11518	0.654932	0.327466	+	0.944863i	$0.393805\pi$
$62$	6.34245	0.805492
$63$	−0.989339	−0.124645
$64$	1.96587	0.245733
$65$	−5.71815	−0.709249
$66$	−8.54121	−1.05135
$67$	−3.84908	−0.470240	−0.235120	−	0.971966i	$-0.575548\pi$
$67$	−3.84908	−0.470240	−0.235120	+	0.971966i	$0.575548\pi$
$68$	−4.93875	−0.598911
$69$	6.12242	0.737053
$70$	−1.78276	−0.213081
$71$	−3.83751	−0.455428	−0.227714	−	0.973728i	$-0.573125\pi$
$71$	−3.83751	−0.455428	−0.227714	+	0.973728i	$0.573125\pi$
$72$	3.13711	0.369712
$73$	−7.45576	−0.872631	−0.436316	−	0.899794i	$-0.643717\pi$
$73$	−7.45576	−0.872631	−0.436316	+	0.899794i	$0.643717\pi$
$74$	2.28873	0.266059
$75$	−2.18505	−0.252307
$76$	2.42235	0.277863
$77$	−2.58387	−0.294459
$78$	6.37312	0.721613
$79$	13.3934	1.50688	0.753440	−	0.657517i	$-0.228393\pi$
$79$	13.3934	1.50688	0.753440	+	0.657517i	$0.228393\pi$
$80$	8.79617	0.983442
$81$	−1.23929	−0.137699
$82$	−19.0703	−2.10596
$83$	7.79301	0.855394	0.427697	−	0.903922i	$-0.359325\pi$
$83$	7.79301	0.855394	0.427697	+	0.903922i	$0.359325\pi$
$84$	0.612483	0.0668274
$85$	9.77199	1.05992
$86$	0	0
$87$	−11.3980	−1.22200
$88$	8.19324	0.873402
$89$	4.50944	0.477999	0.239000	−	0.971020i	$-0.423180\pi$
$89$	4.50944	0.477999	0.239000	+	0.971020i	$0.423180\pi$
$90$	4.98929	0.525918
$91$	1.92798	0.202107
$92$	4.72065	0.492162
$93$	4.31146	0.447078
$94$	6.95057	0.716897
$95$	−4.79295	−0.491747
$96$	−5.44534	−0.555763
$97$	0.184960	0.0187798	0.00938992	−	0.999956i	$-0.497011\pi$
$97$	0.184960	0.0187798	0.00938992	+	0.999956i	$0.497011\pi$
$98$	−11.3014	−1.14162
$99$	7.23130	0.726773
$100$	−1.68476	−0.168476
$101$	4.12809	0.410760	0.205380	−	0.978682i	$-0.434157\pi$
$101$	4.12809	0.410760	0.205380	+	0.978682i	$0.434157\pi$
$102$	−10.8913	−1.07840
$103$	15.7336	1.55028	0.775141	−	0.631788i	$-0.217679\pi$
$103$	15.7336	1.55028	0.775141	+	0.631788i	$0.217679\pi$
$104$	−6.11347	−0.599475
$105$	−1.21188	−0.118268
$106$	−4.09952	−0.398180
$107$	0.0534833	0.00517043	0.00258521	−	0.999997i	$-0.499177\pi$
$107$	0.0534833	0.00517043	0.00258521	+	0.999997i	$0.499177\pi$
$108$	−4.80453	−0.462316
$109$	−5.25004	−0.502863	−0.251431	−	0.967875i	$-0.580901\pi$
$109$	−5.25004	−0.502863	−0.251431	+	0.967875i	$0.580901\pi$
$110$	13.0306	1.24242
$111$	1.55583	0.147673
$112$	−2.96579	−0.280241
$113$	2.58205	0.242899	0.121450	−	0.992598i	$-0.461246\pi$
$113$	2.58205	0.242899	0.121450	+	0.992598i	$0.461246\pi$
$114$	5.34195	0.500319
$115$	−9.34045	−0.871001
$116$	−8.78838	−0.815980
$117$	−5.39571	−0.498833
$118$	−1.24999	−0.115071
$119$	−3.29481	−0.302034
$120$	3.84278	0.350796
$121$	7.88606	0.716914
$122$	8.69765	0.787448
$123$	−12.9636	−1.16889
$124$	3.32432	0.298533
$125$	12.1506	1.08678
$126$	−1.68223	−0.149865
$127$	−13.0649	−1.15933	−0.579663	−	0.814856i	$-0.696816\pi$
$127$	−13.0649	−1.15933	−0.579663	+	0.814856i	$0.696816\pi$
$128$	12.7648	1.12826
$129$	0	0
$130$	−9.72291	−0.852756
$131$	−10.7746	−0.941385	−0.470693	−	0.882297i	$-0.655996\pi$
$131$	−10.7746	−0.941385	−0.470693	+	0.882297i	$0.655996\pi$
$132$	−4.47678	−0.389653
$133$	1.61603	0.140128
$134$	−6.54482	−0.565386
$135$	9.50641	0.818181
$136$	10.4476	0.895871
$137$	−8.03721	−0.686665	−0.343333	−	0.939214i	$-0.611556\pi$
$137$	−8.03721	−0.686665	−0.343333	+	0.939214i	$0.611556\pi$
$138$	10.4103	0.886185
$139$	21.8884	1.85655	0.928274	−	0.371896i	$-0.121292\pi$
$139$	21.8884	1.85655	0.928274	+	0.371896i	$0.121292\pi$
$140$	−0.934413	−0.0789723
$141$	4.72485	0.397904
$142$	−6.52514	−0.547578
$143$	−14.0920	−1.17843
$144$	8.30016	0.691680
$145$	17.3890	1.44408
$146$	−12.6775	−1.04920
$147$	−7.68246	−0.633639
$148$	1.19961	0.0986073
$149$	−16.5094	−1.35250	−0.676250	−	0.736672i	$-0.736396\pi$
$149$	−16.5094	−1.35250	−0.676250	+	0.736672i	$0.736396\pi$
$150$	−3.71536	−0.303358
$151$	15.8693	1.29142	0.645711	−	0.763582i	$-0.276561\pi$
$151$	15.8693	1.29142	0.645711	+	0.763582i	$0.276561\pi$
$152$	−5.12431	−0.415636
$153$	9.22095	0.745470
$154$	−4.39350	−0.354039
$155$	−6.57762	−0.528327
$156$	3.34039	0.267446
$157$	−6.56626	−0.524045	−0.262022	−	0.965062i	$-0.584389\pi$
$157$	−6.56626	−0.524045	−0.262022	+	0.965062i	$0.584389\pi$
$158$	22.7737	1.81178
$159$	−2.78676	−0.221005
$160$	8.30749	0.656764
$161$	3.14931	0.248200
$162$	−2.10724	−0.165561
$163$	−12.7026	−0.994944	−0.497472	−	0.867480i	$-0.665738\pi$
$163$	−12.7026	−0.994944	−0.497472	+	0.867480i	$0.665738\pi$
$164$	−9.99549	−0.780516
$165$	8.85791	0.689588
$166$	13.2509	1.02847
$167$	16.6713	1.29006	0.645032	−	0.764155i	$-0.276844\pi$
$167$	16.6713	1.29006	0.645032	+	0.764155i	$0.276844\pi$
$168$	−1.29566	−0.0999627
$169$	−2.48508	−0.191160
$170$	16.6159	1.27438
$171$	−4.52268	−0.345858
$172$	0	0
$173$	8.10129	0.615930	0.307965	−	0.951398i	$-0.400352\pi$
$173$	8.10129	0.615930	0.307965	+	0.951398i	$0.400352\pi$
$174$	−19.3808	−1.46925
$175$	−1.12396	−0.0849636
$176$	21.6776	1.63401
$177$	−0.849718	−0.0638687
$178$	7.66767	0.574716
$179$	−17.4497	−1.30425	−0.652125	−	0.758111i	$-0.726122\pi$
$179$	−17.4497	−1.30425	−0.652125	+	0.758111i	$0.726122\pi$
$180$	2.61508	0.194916
$181$	14.1146	1.04913	0.524567	−	0.851369i	$-0.324227\pi$
$181$	14.1146	1.04913	0.524567	+	0.851369i	$0.324227\pi$
$182$	3.27826	0.243001
$183$	5.91247	0.437063
$184$	−9.98619	−0.736192
$185$	−2.37359	−0.174510
$186$	7.33104	0.537538
$187$	24.0825	1.76108
$188$	3.64306	0.265698
$189$	−3.20526	−0.233148
$190$	−8.14975	−0.591245
$191$	−18.9502	−1.37119	−0.685595	−	0.727983i	$-0.740458\pi$
$191$	−18.9502	−1.37119	−0.685595	+	0.727983i	$0.740458\pi$
$192$	2.27228	0.163988
$193$	−21.1880	−1.52514	−0.762572	−	0.646903i	$-0.776064\pi$
$193$	−21.1880	−1.52514	−0.762572	+	0.646903i	$0.776064\pi$
$194$	0.314499	0.0225797
$195$	−6.60942	−0.473311
$196$	−5.92351	−0.423108
$197$	2.82273	0.201111	0.100556	−	0.994931i	$-0.467938\pi$
$197$	2.82273	0.201111	0.100556	+	0.994931i	$0.467938\pi$
$198$	12.2958	0.873825
$199$	−0.0129904	−0.000920863 0	−0.000460431	−	1.00000i	$-0.500147\pi$
$199$	−0.0129904	−0.000920863 0	−0.000460431		1.00000i	$0.500147\pi$
$200$	3.56400	0.252013
$201$	−4.44902	−0.313810
$202$	7.01924	0.493872
$203$	−5.86302	−0.411503
$204$	−5.70854	−0.399678
$205$	19.7774	1.38132
$206$	26.7529	1.86396
$207$	−8.81375	−0.612598
$208$	−16.1750	−1.12153
$209$	−11.8119	−0.817049
$210$	−2.06064	−0.142197
$211$	−2.16836	−0.149276	−0.0746380	−	0.997211i	$-0.523780\pi$
$211$	−2.16836	−0.149276	−0.0746380	+	0.997211i	$0.523780\pi$
$212$	−2.14871	−0.147574
$213$	−4.43565	−0.303926
$214$	0.0909409	0.00621659
$215$	0	0
$216$	10.1636	0.691547
$217$	2.21777	0.150552
$218$	−8.92696	−0.604610
$219$	−8.61787	−0.582342
$220$	6.82983	0.460467
$221$	−17.9694	−1.20875
$222$	2.64546	0.177552
$223$	3.77604	0.252862	0.126431	−	0.991975i	$-0.459648\pi$
$223$	3.77604	0.252862	0.126431	+	0.991975i	$0.459648\pi$
$224$	−2.80102	−0.187151
$225$	3.14556	0.209704
$226$	4.39042	0.292046
$227$	−16.5799	−1.10045	−0.550224	−	0.835017i	$-0.685458\pi$
$227$	−16.5799	−1.10045	−0.550224	+	0.835017i	$0.685458\pi$
$228$	2.79992	0.185429
$229$	−0.773978	−0.0511459	−0.0255730	−	0.999673i	$-0.508141\pi$
$229$	−0.773978	−0.0511459	−0.0255730	+	0.999673i	$0.508141\pi$
$230$	−15.8821	−1.04724
$231$	−2.98661	−0.196504
$232$	18.5912	1.22057
$233$	−25.9761	−1.70175	−0.850876	−	0.525366i	$-0.823928\pi$
$233$	−25.9761	−1.70175	−0.850876	+	0.525366i	$0.823928\pi$
$234$	−9.17465	−0.599765
$235$	−7.20829	−0.470217
$236$	−0.655169	−0.0426479
$237$	15.4810	1.00560
$238$	−5.60236	−0.363147
$239$	3.52561	0.228053	0.114026	−	0.993478i	$-0.463625\pi$
$239$	3.52561	0.228053	0.114026	+	0.993478i	$0.463625\pi$
$240$	10.1672	0.656291
$241$	−19.5154	−1.25710	−0.628549	−	0.777770i	$-0.716351\pi$
$241$	−19.5154	−1.25710	−0.628549	+	0.777770i	$0.716351\pi$
$242$	13.4091	0.861972
$243$	14.7403	0.945593
$244$	4.55877	0.291845
$245$	11.7205	0.748793
$246$	−22.0428	−1.40540
$247$	8.81360	0.560796
$248$	−7.03236	−0.446555
$249$	9.00769	0.570839
$250$	20.6603	1.30667
$251$	8.90689	0.562198	0.281099	−	0.959679i	$-0.409301\pi$
$251$	8.90689	0.562198	0.281099	+	0.959679i	$0.409301\pi$
$252$	−0.881722	−0.0555433
$253$	−23.0190	−1.44719
$254$	−22.2151	−1.39390
$255$	11.2951	0.707328
$256$	17.7730	1.11081
$257$	0.0980769	0.00611787	0.00305893	−	0.999995i	$-0.499026\pi$
$257$	0.0980769	0.00611787	0.00305893	+	0.999995i	$0.499026\pi$
$258$	0	0
$259$	0.800300	0.0497282
$260$	−5.09615	−0.316050
$261$	16.4084	1.01566
$262$	−18.3208	−1.13186
$263$	−0.463866	−0.0286032	−0.0143016	−	0.999898i	$-0.504552\pi$
$263$	−0.463866	−0.0286032	−0.0143016	+	0.999898i	$0.504552\pi$
$264$	9.47030	0.582856
$265$	4.25152	0.261169
$266$	2.74784	0.168481
$267$	5.21231	0.318988
$268$	−3.43039	−0.209544
$269$	21.4271	1.30643	0.653216	−	0.757171i	$-0.273419\pi$
$269$	21.4271	1.30643	0.653216	+	0.757171i	$0.273419\pi$
$270$	16.1643	0.983729
$271$	−9.45879	−0.574581	−0.287290	−	0.957844i	$-0.592754\pi$
$271$	−9.45879	−0.574581	−0.287290	+	0.957844i	$0.592754\pi$
$272$	27.6421	1.67605
$273$	2.22849	0.134874
$274$	−13.6662	−0.825603
$275$	8.21530	0.495401
$276$	5.45645	0.328440
$277$	12.7119	0.763785	0.381893	−	0.924207i	$-0.375272\pi$
$277$	12.7119	0.763785	0.381893	+	0.924207i	$0.375272\pi$
$278$	37.2181	2.23219
$279$	−6.20672	−0.371586
$280$	1.97668	0.118129
$281$	19.4455	1.16002	0.580011	−	0.814609i	$-0.303048\pi$
$281$	19.4455	1.16002	0.580011	+	0.814609i	$0.303048\pi$
$282$	8.03394	0.478414
$283$	2.46628	0.146605	0.0733026	−	0.997310i	$-0.476646\pi$
$283$	2.46628	0.146605	0.0733026	+	0.997310i	$0.476646\pi$
$284$	−3.42008	−0.202944
$285$	−5.54002	−0.328162
$286$	−23.9615	−1.41687
$287$	−6.66833	−0.393619
$288$	7.83903	0.461919
$289$	13.7086	0.806390
$290$	29.5676	1.73627
$291$	0.213789	0.0125325
$292$	−6.64475	−0.388855
$293$	−21.7907	−1.27303	−0.636515	−	0.771265i	$-0.719624\pi$
$293$	−21.7907	−1.27303	−0.636515	+	0.771265i	$0.719624\pi$
$294$	−13.0630	−0.761847
$295$	1.29634	0.0754759
$296$	−2.53769	−0.147500
$297$	23.4280	1.35943
$298$	−28.0719	−1.62616
$299$	17.1758	0.993305
$300$	−1.94736	−0.112431
$301$	0	0
$302$	26.9834	1.55272
$303$	4.77153	0.274117
$304$	−13.5579	−0.777598
$305$	−9.02015	−0.516492
$306$	15.6789	0.896305
$307$	−19.9355	−1.13778	−0.568890	−	0.822414i	$-0.692627\pi$
$307$	−19.9355	−1.13778	−0.568890	+	0.822414i	$0.692627\pi$
$308$	−2.30280	−0.131214
$309$	18.1860	1.03457
$310$	−11.1843	−0.635227
$311$	−5.89502	−0.334276	−0.167138	−	0.985934i	$-0.553453\pi$
$311$	−5.89502	−0.334276	−0.167138	+	0.985934i	$0.553453\pi$
$312$	−7.06636	−0.400054
$313$	20.9619	1.18484	0.592418	−	0.805631i	$-0.298174\pi$
$313$	20.9619	1.18484	0.592418	+	0.805631i	$0.298174\pi$
$314$	−11.1650	−0.630078
$315$	1.74461	0.0982975
$316$	11.9366	0.671484
$317$	21.7222	1.22004	0.610019	−	0.792387i	$-0.291162\pi$
$317$	21.7222	1.22004	0.610019	+	0.792387i	$0.291162\pi$
$318$	−4.73850	−0.265722
$319$	42.8541	2.39937
$320$	−3.46663	−0.193790
$321$	0.0618196	0.00345043
$322$	5.35495	0.298420
$323$	−15.0619	−0.838069
$324$	−1.10449	−0.0613604
$325$	−6.12993	−0.340027
$326$	−21.5990	−1.19626
$327$	−6.06835	−0.335581
$328$	21.1447	1.16752
$329$	2.43041	0.133993
$330$	15.0616	0.829116
$331$	−9.48307	−0.521237	−0.260618	−	0.965442i	$-0.583926\pi$
$331$	−9.48307	−0.521237	−0.260618	+	0.965442i	$0.583926\pi$
$332$	6.94532	0.381174
$333$	−2.23975	−0.122737
$334$	28.3472	1.55109
$335$	6.78749	0.370840
$336$	−3.42806	−0.187016
$337$	−24.9983	−1.36174	−0.680872	−	0.732402i	$-0.738399\pi$
$337$	−24.9983	−1.36174	−0.680872	+	0.732402i	$0.738399\pi$
$338$	−4.22554	−0.229839
$339$	2.98451	0.162096
$340$	8.70902	0.472313
$341$	−16.2102	−0.877829
$342$	−7.69019	−0.415838
$343$	−8.11373	−0.438100
$344$	0	0
$345$	−10.7963	−0.581255
$346$	13.7751	0.740555
$347$	−10.2429	−0.549867	−0.274934	−	0.961463i	$-0.588656\pi$
$347$	−10.2429	−0.549867	−0.274934	+	0.961463i	$0.588656\pi$
$348$	−10.1582	−0.544537
$349$	−14.7987	−0.792158	−0.396079	−	0.918216i	$-0.629629\pi$
$349$	−14.7987	−0.792158	−0.396079	+	0.918216i	$0.629629\pi$
$350$	−1.91114	−0.102155
$351$	−17.4810	−0.933068
$352$	20.4733	1.09123
$353$	−12.0266	−0.640114	−0.320057	−	0.947398i	$-0.603702\pi$
$353$	−12.0266	−0.640114	−0.320057	+	0.947398i	$0.603702\pi$
$354$	−1.44483	−0.0767917
$355$	6.76709	0.359160
$356$	4.01892	0.213002
$357$	−3.80836	−0.201560
$358$	−29.6707	−1.56815
$359$	7.70345	0.406573	0.203286	−	0.979119i	$-0.434838\pi$
$359$	7.70345	0.406573	0.203286	+	0.979119i	$0.434838\pi$
$360$	−5.53201	−0.291563
$361$	−11.6124	−0.611181
$362$	24.0000	1.26141
$363$	9.11524	0.478426
$364$	1.71826	0.0900614
$365$	13.1475	0.688174
$366$	10.0533	0.525496
$367$	3.21531	0.167838	0.0839190	−	0.996473i	$-0.473256\pi$
$367$	3.21531	0.167838	0.0839190	+	0.996473i	$0.473256\pi$
$368$	−26.4214	−1.37731
$369$	18.6622	0.971515
$370$	−4.03596	−0.209819
$371$	−1.43348	−0.0744226
$372$	3.84248	0.199223
$373$	−17.6170	−0.912173	−0.456086	−	0.889936i	$-0.650749\pi$
$373$	−17.6170	−0.912173	−0.456086	+	0.889936i	$0.650749\pi$
$374$	40.9488	2.11741
$375$	14.0445	0.725252
$376$	−7.70663	−0.397439
$377$	−31.9761	−1.64685
$378$	−5.45010	−0.280323
$379$	17.6797	0.908145	0.454072	−	0.890965i	$-0.349971\pi$
$379$	17.6797	0.908145	0.454072	+	0.890965i	$0.349971\pi$
$380$	−4.27159	−0.219128
$381$	−15.1013	−0.773665
$382$	−32.2222	−1.64863
$383$	24.8944	1.27205	0.636023	−	0.771670i	$-0.280578\pi$
$383$	24.8944	1.27205	0.636023	+	0.771670i	$0.280578\pi$
$384$	14.7544	0.752931
$385$	4.55641	0.232216
$386$	−36.0272	−1.83374
$387$	0	0
$388$	0.164841	0.00836852
$389$	−6.72429	−0.340935	−0.170467	−	0.985363i	$-0.554528\pi$
$389$	−6.72429	−0.340935	−0.170467	+	0.985363i	$0.554528\pi$
$390$	−11.2384	−0.569078
$391$	−29.3525	−1.48442
$392$	12.5308	0.632899
$393$	−12.4541	−0.628224
$394$	4.79966	0.241803
$395$	−23.6181	−1.18836
$396$	6.44470	0.323858
$397$	−20.3490	−1.02129	−0.510644	−	0.859792i	$-0.670593\pi$
$397$	−20.3490	−1.02129	−0.510644	+	0.859792i	$0.670593\pi$
$398$	−0.0220883	−0.00110719
$399$	1.86792	0.0935130
$400$	9.42961	0.471480
$401$	0.193055	0.00964071	0.00482036	−	0.999988i	$-0.498466\pi$
$401$	0.193055	0.00964071	0.00482036	+	0.999988i	$0.498466\pi$
$402$	−7.56494	−0.377305
$403$	12.0954	0.602513
$404$	3.67905	0.183040
$405$	2.18538	0.108592
$406$	−9.96925	−0.494765
$407$	−5.84957	−0.289952
$408$	12.0760	0.597851
$409$	−0.492305	−0.0243429	−0.0121715	−	0.999926i	$-0.503874\pi$
$409$	−0.492305	−0.0243429	−0.0121715	+	0.999926i	$0.503874\pi$
$410$	33.6287	1.66081
$411$	−9.28995	−0.458240
$412$	14.0222	0.690824
$413$	−0.437086	−0.0215076
$414$	−14.9865	−0.736549
$415$	−13.7423	−0.674581
$416$	−15.2764	−0.748985
$417$	25.3001	1.23895
$418$	−20.0846	−0.982367
$419$	−16.0780	−0.785463	−0.392732	−	0.919653i	$-0.628470\pi$
$419$	−16.0780	−0.785463	−0.392732	+	0.919653i	$0.628470\pi$
$420$	−1.08006	−0.0527014
$421$	−36.4314	−1.77556	−0.887779	−	0.460271i	$-0.847752\pi$
$421$	−36.4314	−1.77556	−0.887779	+	0.460271i	$0.847752\pi$
$422$	−3.68699	−0.179480
$423$	−6.80182	−0.330716
$424$	4.54545	0.220746
$425$	10.4757	0.508146
$426$	−7.54220	−0.365421
$427$	3.04131	0.147179
$428$	0.0476656	0.00230400
$429$	−16.2885	−0.786417
$430$	0	0
$431$	8.13149	0.391680	0.195840	−	0.980636i	$-0.437257\pi$
$431$	8.13149	0.391680	0.195840	+	0.980636i	$0.437257\pi$
$432$	26.8909	1.29379
$433$	−27.5411	−1.32354	−0.661770	−	0.749707i	$-0.730194\pi$
$433$	−27.5411	−1.32354	−0.661770	+	0.749707i	$0.730194\pi$
$434$	3.77100	0.181014
$435$	20.0994	0.963691
$436$	−4.67896	−0.224082
$437$	14.3968	0.688692
$438$	−14.6535	−0.700171
$439$	−37.2707	−1.77883	−0.889416	−	0.457099i	$-0.848889\pi$
$439$	−37.2707	−1.77883	−0.889416	+	0.457099i	$0.848889\pi$
$440$	−14.4480	−0.688782
$441$	11.0596	0.526646
$442$	−30.5544	−1.45333
$443$	−5.47448	−0.260101	−0.130050	−	0.991507i	$-0.541514\pi$
$443$	−5.47448	−0.260101	−0.130050	+	0.991507i	$0.541514\pi$
$444$	1.38659	0.0658046
$445$	−7.95198	−0.376960
$446$	6.42063	0.304026
$447$	−19.0826	−0.902578
$448$	1.16884	0.0552224
$449$	22.7304	1.07271	0.536356	−	0.843992i	$-0.319800\pi$
$449$	22.7304	1.07271	0.536356	+	0.843992i	$0.319800\pi$
$450$	5.34859	0.252135
$451$	48.7403	2.29509
$452$	2.30119	0.108239
$453$	18.3428	0.861818
$454$	−28.1918	−1.32311
$455$	−3.39981	−0.159386
$456$	−5.92302	−0.277371
$457$	−33.1117	−1.54890	−0.774449	−	0.632636i	$-0.781973\pi$
$457$	−33.1117	−1.54890	−0.774449	+	0.632636i	$0.781973\pi$
$458$	−1.31604	−0.0614946
$459$	29.8740	1.39440
$460$	−8.32443	−0.388129
$461$	−14.9822	−0.697790	−0.348895	−	0.937162i	$-0.613443\pi$
$461$	−14.9822	−0.697790	−0.348895	+	0.937162i	$0.613443\pi$
$462$	−5.07831	−0.236264
$463$	18.2384	0.847609	0.423805	−	0.905754i	$-0.360694\pi$
$463$	18.2384	0.847609	0.423805	+	0.905754i	$0.360694\pi$
$464$	49.1884	2.28352
$465$	−7.60286	−0.352574
$466$	−44.1688	−2.04608
$467$	3.47982	0.161027	0.0805135	−	0.996754i	$-0.474344\pi$
$467$	3.47982	0.161027	0.0805135	+	0.996754i	$0.474344\pi$
$468$	−4.80878	−0.222286
$469$	−2.28853	−0.105674
$470$	−12.2567	−0.565359
$471$	−7.58973	−0.349716
$472$	1.38596	0.0637941
$473$	0	0
$474$	26.3233	1.20907
$475$	−5.13811	−0.235753
$476$	−2.93641	−0.134590
$477$	4.01178	0.183687
$478$	5.99481	0.274196
$479$	23.9869	1.09599	0.547994	−	0.836482i	$-0.315391\pi$
$479$	23.9869	1.09599	0.547994	+	0.836482i	$0.315391\pi$
$480$	9.60235	0.438285
$481$	4.36472	0.199014
$482$	−33.1832	−1.51145
$483$	3.64018	0.165634
$484$	7.02824	0.319465
$485$	−0.326160	−0.0148102
$486$	25.0639	1.13692
$487$	−4.42005	−0.200291	−0.100146	−	0.994973i	$-0.531931\pi$
$487$	−4.42005	−0.200291	−0.100146	+	0.994973i	$0.531931\pi$
$488$	−9.64375	−0.436552
$489$	−14.6825	−0.663967
$490$	19.9290	0.900301
$491$	15.6570	0.706590	0.353295	−	0.935512i	$-0.385061\pi$
$491$	15.6570	0.706590	0.353295	+	0.935512i	$0.385061\pi$
$492$	−11.5535	−0.520870
$493$	54.6452	2.46110
$494$	14.9863	0.674265
$495$	−12.7517	−0.573147
$496$	−18.6062	−0.835443
$497$	−2.28165	−0.102346
$498$	15.3163	0.686341
$499$	37.6600	1.68589	0.842947	−	0.537996i	$-0.180819\pi$
$499$	37.6600	1.68589	0.842947	+	0.537996i	$0.180819\pi$
$500$	10.8289	0.484282
$501$	19.2698	0.860912
$502$	15.1449	0.675951
$503$	−31.0430	−1.38414	−0.692070	−	0.721830i	$-0.743301\pi$
$503$	−31.0430	−1.38414	−0.692070	+	0.721830i	$0.743301\pi$
$504$	1.86522	0.0830835
$505$	−7.27951	−0.323934
$506$	−39.1405	−1.74001
$507$	−2.87243	−0.127569
$508$	−11.6438	−0.516609
$509$	4.65215	0.206203	0.103101	−	0.994671i	$-0.467123\pi$
$509$	4.65215	0.206203	0.103101	+	0.994671i	$0.467123\pi$
$510$	19.2058	0.850446
$511$	−4.43294	−0.196102
$512$	4.69090	0.207310
$513$	−14.6526	−0.646928
$514$	0.166766	0.00735573
$515$	−27.7448	−1.22258
$516$	0	0
$517$	−17.7644	−0.781277
$518$	1.36080	0.0597900
$519$	9.36402	0.411035
$520$	10.7805	0.472758
$521$	−7.07583	−0.309998	−0.154999	−	0.987915i	$-0.549537\pi$
$521$	−7.07583	−0.309998	−0.154999	+	0.987915i	$0.549537\pi$
$522$	27.9003	1.22116
$523$	4.41270	0.192954	0.0964770	−	0.995335i	$-0.469243\pi$
$523$	4.41270	0.192954	0.0964770	+	0.995335i	$0.469243\pi$
$524$	−9.60262	−0.419492
$525$	−1.29915	−0.0566997
$526$	−0.788739	−0.0343906
$527$	−20.6703	−0.900412
$528$	25.0565	1.09044
$529$	5.05630	0.219839
$530$	7.22912	0.314013
$531$	1.22324	0.0530842
$532$	1.44025	0.0624426
$533$	−36.3681	−1.57528
$534$	8.86281	0.383531
$535$	−0.0943128	−0.00407750
$536$	7.25674	0.313443
$537$	−20.1695	−0.870379
$538$	36.4338	1.57077
$539$	28.8844	1.24414
$540$	8.47234	0.364591
$541$	−17.0661	−0.733729	−0.366864	−	0.930274i	$-0.619569\pi$
$541$	−17.0661	−0.733729	−0.366864	+	0.930274i	$0.619569\pi$
$542$	−16.0834	−0.690839
$543$	16.3147	0.700129
$544$	26.1064	1.11930
$545$	9.25796	0.396567
$546$	3.78923	0.162164
$547$	10.2005	0.436140	0.218070	−	0.975933i	$-0.430024\pi$
$547$	10.2005	0.436140	0.218070	+	0.975933i	$0.430024\pi$
$548$	−7.16295	−0.305986
$549$	−8.51151	−0.363262
$550$	13.9690	0.595638
$551$	−26.8023	−1.14182
$552$	−11.5427	−0.491291
$553$	7.96328	0.338633
$554$	21.6148	0.918326
$555$	−2.74356	−0.116457
$556$	19.5074	0.827300
$557$	31.3958	1.33028	0.665142	−	0.746717i	$-0.268371\pi$
$557$	31.3958	1.33028	0.665142	+	0.746717i	$0.268371\pi$
$558$	−10.5537	−0.446772
$559$	0	0
$560$	5.22990	0.221004
$561$	27.8361	1.17524
$562$	33.0644	1.39474
$563$	−37.7263	−1.58998	−0.794988	−	0.606625i	$-0.792523\pi$
$563$	−37.7263	−1.58998	−0.794988	+	0.606625i	$0.792523\pi$
$564$	4.21090	0.177311
$565$	−4.55321	−0.191555
$566$	4.19357	0.176269
$567$	−0.736841	−0.0309444
$568$	7.23492	0.303571
$569$	3.61706	0.151635	0.0758175	−	0.997122i	$-0.475843\pi$
$569$	3.61706	0.151635	0.0758175	+	0.997122i	$0.475843\pi$
$570$	−9.42003	−0.394562
$571$	15.3842	0.643808	0.321904	−	0.946772i	$-0.395677\pi$
$571$	15.3842	0.643808	0.321904	+	0.946772i	$0.395677\pi$
$572$	−12.5592	−0.525124
$573$	−21.9039	−0.915050
$574$	−11.3386	−0.473262
$575$	−10.0131	−0.417574
$576$	−3.27115	−0.136298
$577$	31.8469	1.32580	0.662902	−	0.748707i	$-0.269325\pi$
$577$	31.8469	1.32580	0.662902	+	0.748707i	$0.269325\pi$
$578$	23.3096	0.969551
$579$	−24.4905	−1.01779
$580$	15.4975	0.643498
$581$	4.63346	0.192228
$582$	0.363519	0.0150683
$583$	10.4776	0.433939
$584$	14.0565	0.581662
$585$	9.51483	0.393390
$586$	−37.0521	−1.53061
$587$	18.5935	0.767436	0.383718	−	0.923450i	$-0.374644\pi$
$587$	18.5935	0.767436	0.383718	+	0.923450i	$0.374644\pi$
$588$	−6.84679	−0.282357
$589$	10.1383	0.417743
$590$	2.20425	0.0907474
$591$	3.26271	0.134210
$592$	−6.71420	−0.275952
$593$	3.43324	0.140986	0.0704932	−	0.997512i	$-0.477543\pi$
$593$	3.43324	0.140986	0.0704932	+	0.997512i	$0.477543\pi$
$594$	39.8360	1.63449
$595$	5.81008	0.238190
$596$	−14.7135	−0.602690
$597$	−0.0150151	−0.000614529 0
$598$	29.2051	1.19429
$599$	18.7285	0.765224	0.382612	−	0.923909i	$-0.375025\pi$
$599$	18.7285	0.765224	0.382612	+	0.923909i	$0.375025\pi$
$600$	4.11951	0.168178
$601$	−4.01565	−0.163802	−0.0819010	−	0.996640i	$-0.526099\pi$
$601$	−4.01565	−0.163802	−0.0819010	+	0.996640i	$0.526099\pi$
$602$	0	0
$603$	6.40475	0.260822
$604$	14.1431	0.575473
$605$	−13.9063	−0.565373
$606$	8.11331	0.329581
$607$	25.5121	1.03550	0.517751	−	0.855531i	$-0.326769\pi$
$607$	25.5121	1.03550	0.517751	+	0.855531i	$0.326769\pi$
$608$	−12.8046	−0.519297
$609$	−6.77688	−0.274613
$610$	−15.3375	−0.620997
$611$	13.2551	0.536243
$612$	8.21793	0.332190
$613$	−17.7223	−0.715797	−0.357899	−	0.933760i	$-0.616507\pi$
$613$	−17.7223	−0.715797	−0.357899	+	0.933760i	$0.616507\pi$
$614$	−33.8975	−1.36799
$615$	22.8601	0.921808
$616$	4.87141	0.196275
$617$	13.4716	0.542345	0.271172	−	0.962531i	$-0.412589\pi$
$617$	13.4716	0.542345	0.271172	+	0.962531i	$0.412589\pi$
$618$	30.9228	1.24390
$619$	30.3811	1.22112	0.610561	−	0.791970i	$-0.290944\pi$
$619$	30.3811	1.22112	0.610561	+	0.791970i	$0.290944\pi$
$620$	−5.86213	−0.235429
$621$	−28.5548	−1.14586
$622$	−10.0237	−0.401912
$623$	2.68116	0.107418
$624$	−18.6961	−0.748445
$625$	−11.9744	−0.478977
$626$	35.6427	1.42457
$627$	−13.6530	−0.545250
$628$	−5.85201	−0.233520
$629$	−7.45905	−0.297412
$630$	2.96646	0.118187
$631$	−5.77209	−0.229783	−0.114892	−	0.993378i	$-0.536652\pi$
$631$	−5.77209	−0.229783	−0.114892	+	0.993378i	$0.536652\pi$
$632$	−25.2509	−1.00443
$633$	−2.50634	−0.0996179
$634$	36.9355	1.46690
$635$	23.0388	0.914267
$636$	−2.48363	−0.0984823
$637$	−21.5524	−0.853937
$638$	72.8674	2.88485
$639$	6.38549	0.252606
$640$	−22.5095	−0.889765
$641$	−12.0345	−0.475333	−0.237666	−	0.971347i	$-0.576383\pi$
$641$	−12.0345	−0.475333	−0.237666	+	0.971347i	$0.576383\pi$
$642$	0.105116	0.00414858
$643$	−42.5459	−1.67785	−0.838923	−	0.544250i	$-0.816814\pi$
$643$	−42.5459	−1.67785	−0.838923	+	0.544250i	$0.816814\pi$
$644$	2.80674	0.110601
$645$	0	0
$646$	−25.6107	−1.00764
$647$	−28.9612	−1.13858	−0.569291	−	0.822136i	$-0.692782\pi$
$647$	−28.9612	−1.13858	−0.569291	+	0.822136i	$0.692782\pi$
$648$	2.33646	0.0917849
$649$	3.19476	0.125405
$650$	−10.4231	−0.408827
$651$	2.56345	0.100469
$652$	−11.3209	−0.443359
$653$	−2.68809	−0.105193	−0.0525966	−	0.998616i	$-0.516750\pi$
$653$	−2.68809	−0.105193	−0.0525966	+	0.998616i	$0.516750\pi$
$654$	−10.3184	−0.403481
$655$	19.0001	0.742395
$656$	55.9446	2.18427
$657$	12.4062	0.484011
$658$	4.13257	0.161104
$659$	7.80448	0.304019	0.152010	−	0.988379i	$-0.451426\pi$
$659$	7.80448	0.304019	0.152010	+	0.988379i	$0.451426\pi$
$660$	7.89438	0.307288
$661$	3.39429	0.132022	0.0660112	−	0.997819i	$-0.478973\pi$
$661$	3.39429	0.132022	0.0660112	+	0.997819i	$0.478973\pi$
$662$	−16.1246	−0.626701
$663$	−20.7702	−0.806649
$664$	−14.6923	−0.570172
$665$	−2.84972	−0.110508
$666$	−3.80837	−0.147571
$667$	−52.2321	−2.02243
$668$	14.8579	0.574868
$669$	4.36460	0.168745
$670$	11.5412	0.445875
$671$	−22.2296	−0.858164
$672$	−3.23761	−0.124894
$673$	−16.2674	−0.627062	−0.313531	−	0.949578i	$-0.601512\pi$
$673$	−16.2674	−0.627062	−0.313531	+	0.949578i	$0.601512\pi$
$674$	−42.5061	−1.63727
$675$	10.1910	0.392251
$676$	−2.21477	−0.0851833
$677$	2.40528	0.0924423	0.0462211	−	0.998931i	$-0.485282\pi$
$677$	2.40528	0.0924423	0.0462211	+	0.998931i	$0.485282\pi$
$678$	5.07474	0.194894
$679$	0.109971	0.00422029
$680$	−18.4233	−0.706502
$681$	−19.1642	−0.734373
$682$	−27.5631	−1.05545
$683$	4.78972	0.183273	0.0916367	−	0.995793i	$-0.470790\pi$
$683$	4.78972	0.183273	0.0916367	+	0.995793i	$0.470790\pi$
$684$	−4.03072	−0.154119
$685$	14.1729	0.541518
$686$	−13.7963	−0.526744
$687$	−0.894617	−0.0341318
$688$	0	0
$689$	−7.81798	−0.297841
$690$	−18.3576	−0.698863
$691$	−17.7737	−0.676143	−0.338072	−	0.941120i	$-0.609775\pi$
$691$	−17.7737	−0.676143	−0.338072	+	0.941120i	$0.609775\pi$
$692$	7.22006	0.274466
$693$	4.29948	0.163324
$694$	−17.4166	−0.661125
$695$	−38.5981	−1.46411
$696$	21.4889	0.814536
$697$	62.1509	2.35413
$698$	−25.1632	−0.952440
$699$	−30.0250	−1.13565
$700$	−1.00170	−0.0378608
$701$	2.59973	0.0981903	0.0490952	−	0.998794i	$-0.484366\pi$
$701$	2.59973	0.0981903	0.0490952	+	0.998794i	$0.484366\pi$
$702$	−29.7240	−1.12186
$703$	3.65851	0.137983
$704$	−8.54329	−0.321987
$705$	−8.33183	−0.313795
$706$	−20.4496	−0.769632
$707$	2.45442	0.0923080
$708$	−0.757289	−0.0284607
$709$	−38.4152	−1.44271	−0.721356	−	0.692564i	$-0.756481\pi$
$709$	−38.4152	−1.44271	−0.721356	+	0.692564i	$0.756481\pi$
$710$	11.5065	0.431831
$711$	−22.2863	−0.835801
$712$	−8.50173	−0.318616
$713$	19.7575	0.739923
$714$	−6.47558	−0.242343
$715$	24.8500	0.929337
$716$	−15.5516	−0.581190
$717$	4.07514	0.152189
$718$	13.0986	0.488837
$719$	33.3797	1.24485	0.622426	−	0.782679i	$-0.286147\pi$
$719$	33.3797	1.24485	0.622426	+	0.782679i	$0.286147\pi$
$720$	−14.6366	−0.545473
$721$	9.35468	0.348387
$722$	−19.7453	−0.734845
$723$	−22.5572	−0.838913
$724$	12.5793	0.467506
$725$	18.6412	0.692318
$726$	15.4992	0.575229
$727$	−36.8788	−1.36776	−0.683880	−	0.729595i	$-0.739709\pi$
$727$	−36.8788	−1.36776	−0.683880	+	0.729595i	$0.739709\pi$
$728$	−3.63486	−0.134717
$729$	20.7558	0.768732
$730$	22.3556	0.827416
$731$	0	0
$732$	5.26934	0.194760
$733$	−26.6921	−0.985894	−0.492947	−	0.870059i	$-0.664080\pi$
$733$	−26.6921	−0.985894	−0.492947	+	0.870059i	$0.664080\pi$
$734$	5.46719	0.201798
$735$	13.5473	0.499700
$736$	−24.9535	−0.919800
$737$	16.7274	0.616160
$738$	31.7324	1.16809
$739$	50.9722	1.87504	0.937520	−	0.347930i	$-0.113115\pi$
$739$	50.9722	1.87504	0.937520	+	0.347930i	$0.113115\pi$
$740$	−2.11540	−0.0777636
$741$	10.1874	0.374242
$742$	−2.43743	−0.0894809
$743$	−20.7948	−0.762886	−0.381443	−	0.924392i	$-0.624573\pi$
$743$	−20.7948	−0.762886	−0.381443	+	0.924392i	$0.624573\pi$
$744$	−8.12848	−0.298004
$745$	29.1127	1.06661
$746$	−29.9552	−1.09674
$747$	−12.9673	−0.474450
$748$	21.4629	0.784760
$749$	0.0317993	0.00116192
$750$	23.8806	0.871997
$751$	10.7184	0.391121	0.195560	−	0.980692i	$-0.437347\pi$
$751$	10.7184	0.391121	0.195560	+	0.980692i	$0.437347\pi$
$752$	−20.3902	−0.743553
$753$	10.2952	0.375177
$754$	−54.3708	−1.98007
$755$	−27.9840	−1.01844
$756$	−2.85660	−0.103894
$757$	−3.34327	−0.121513	−0.0607566	−	0.998153i	$-0.519351\pi$
$757$	−3.34327	−0.121513	−0.0607566	+	0.998153i	$0.519351\pi$
$758$	30.0618	1.09190
$759$	−26.6069	−0.965769
$760$	9.03625	0.327779
$761$	−38.3661	−1.39077	−0.695384	−	0.718638i	$-0.744766\pi$
$761$	−38.3661	−1.39077	−0.695384	+	0.718638i	$0.744766\pi$
$762$	−25.6777	−0.930205
$763$	−3.12149	−0.113006
$764$	−16.8889	−0.611018
$765$	−16.2603	−0.587892
$766$	42.3295	1.52943
$767$	−2.38380	−0.0860740
$768$	20.5432	0.741289
$769$	−0.652284	−0.0235220	−0.0117610	−	0.999931i	$-0.503744\pi$
$769$	−0.652284	−0.0235220	−0.0117610	+	0.999931i	$0.503744\pi$
$770$	7.74754	0.279202
$771$	0.113364	0.00408270
$772$	−18.8832	−0.679622
$773$	43.3995	1.56097	0.780486	−	0.625174i	$-0.214972\pi$
$773$	43.3995	1.56097	0.780486	+	0.625174i	$0.214972\pi$
$774$	0	0
$775$	−7.05130	−0.253290
$776$	−0.348709	−0.0125179
$777$	0.925041	0.0331856
$778$	−11.4337	−0.409918
$779$	−30.4837	−1.09219
$780$	−5.89047	−0.210913
$781$	16.6771	0.596752
$782$	−49.9098	−1.78477
$783$	53.1601	1.89979
$784$	33.1538	1.18406
$785$	11.5790	0.413272
$786$	−21.1764	−0.755337
$787$	−33.4430	−1.19211	−0.596057	−	0.802942i	$-0.703267\pi$
$787$	−33.4430	−1.19211	−0.596057	+	0.802942i	$0.703267\pi$
$788$	2.51569	0.0896176
$789$	−0.536167	−0.0190881
$790$	−40.1593	−1.42880
$791$	1.53520	0.0545854
$792$	−13.6333	−0.484438
$793$	16.5869	0.589016
$794$	−34.6007	−1.22793
$795$	4.91420	0.174289
$796$	−0.0115773	−0.000410347 0
$797$	−34.3345	−1.21619	−0.608096	−	0.793864i	$-0.708066\pi$
$797$	−34.3345	−1.21619	−0.608096	+	0.793864i	$0.708066\pi$
$798$	3.17614	0.112434
$799$	−22.6522	−0.801376
$800$	8.90573	0.314865
$801$	−7.50357	−0.265126
$802$	0.328263	0.0115914
$803$	32.4013	1.14342
$804$	−3.96508	−0.139837
$805$	−5.55351	−0.195735
$806$	20.5665	0.724424
$807$	24.7669	0.871835
$808$	−7.78277	−0.273797
$809$	46.6942	1.64168	0.820841	−	0.571157i	$-0.193505\pi$
$809$	46.6942	1.64168	0.820841	+	0.571157i	$0.193505\pi$
$810$	3.71593	0.130564
$811$	−24.9497	−0.876104	−0.438052	−	0.898950i	$-0.644331\pi$
$811$	−24.9497	−0.876104	−0.438052	+	0.898950i	$0.644331\pi$
$812$	−5.22526	−0.183371
$813$	−10.9331	−0.383441
$814$	−9.94637	−0.348620
$815$	22.3999	0.784633
$816$	31.9506	1.11850
$817$	0	0
$818$	−0.837096	−0.0292684
$819$	−3.20810	−0.112100
$820$	17.6261	0.615531
$821$	54.8527	1.91437	0.957186	−	0.289474i	$-0.0934804\pi$
$821$	54.8527	1.91437	0.957186	+	0.289474i	$0.0934804\pi$
$822$	−15.7963	−0.550958
$823$	27.1455	0.946234	0.473117	−	0.881000i	$-0.343129\pi$
$823$	27.1455	0.946234	0.473117	+	0.881000i	$0.343129\pi$
$824$	−29.6629	−1.03336
$825$	9.49579	0.330601
$826$	−0.743203	−0.0258593
$827$	−4.03843	−0.140430	−0.0702150	−	0.997532i	$-0.522369\pi$
$827$	−4.03843	−0.140430	−0.0702150	+	0.997532i	$0.522369\pi$
$828$	−7.85502	−0.272981
$829$	12.3779	0.429902	0.214951	−	0.976625i	$-0.431041\pi$
$829$	12.3779	0.429902	0.214951	+	0.976625i	$0.431041\pi$
$830$	−23.3668	−0.811073
$831$	14.6933	0.509705
$832$	6.37466	0.221002
$833$	36.8318	1.27615
$834$	43.0192	1.48963
$835$	−29.3983	−1.01737
$836$	−10.5271	−0.364087
$837$	−20.1085	−0.695052
$838$	−27.3384	−0.944391
$839$	32.6896	1.12857	0.564285	−	0.825580i	$-0.309152\pi$
$839$	32.6896	1.12857	0.564285	+	0.825580i	$0.309152\pi$
$840$	2.28478	0.0788325
$841$	68.2398	2.35310
$842$	−61.9465	−2.13482
$843$	22.4764	0.774130
$844$	−1.93249	−0.0665191
$845$	4.38221	0.150753
$846$	−11.5655	−0.397632
$847$	4.68878	0.161108
$848$	12.0263	0.412986
$849$	2.85070	0.0978356
$850$	17.8124	0.610962
$851$	7.12965	0.244401
$852$	−3.95315	−0.135433
$853$	9.16353	0.313753	0.156877	−	0.987618i	$-0.449857\pi$
$853$	9.16353	0.313753	0.156877	+	0.987618i	$0.449857\pi$
$854$	5.17132	0.176959
$855$	7.97533	0.272751
$856$	−0.100833	−0.00344640
$857$	−12.5475	−0.428616	−0.214308	−	0.976766i	$-0.568750\pi$
$857$	−12.5475	−0.428616	−0.214308	+	0.976766i	$0.568750\pi$
$858$	−27.6963	−0.945538
$859$	13.4029	0.457302	0.228651	−	0.973508i	$-0.426568\pi$
$859$	13.4029	0.457302	0.228651	+	0.973508i	$0.426568\pi$
$860$	0	0
$861$	−7.70770	−0.262678
$862$	13.8265	0.470931
$863$	33.1267	1.12765	0.563823	−	0.825896i	$-0.309330\pi$
$863$	33.1267	1.12765	0.563823	+	0.825896i	$0.309330\pi$
$864$	25.3969	0.864020
$865$	−14.2859	−0.485734
$866$	−46.8297	−1.59134
$867$	15.8454	0.538136
$868$	1.97653	0.0670877
$869$	−58.2053	−1.97448
$870$	34.1762	1.15868
$871$	−12.4813	−0.422913
$872$	9.89800	0.335189
$873$	−0.307768	−0.0104164
$874$	24.4797	0.828039
$875$	7.22431	0.244226
$876$	−7.68045	−0.259498
$877$	−0.274175	−0.00925825	−0.00462912	−	0.999989i	$-0.501474\pi$
$877$	−0.274175	−0.00925825	−0.00462912	+	0.999989i	$0.501474\pi$
$878$	−63.3735	−2.13875
$879$	−25.1872	−0.849544
$880$	−38.2265	−1.28861
$881$	−36.2982	−1.22292	−0.611458	−	0.791277i	$-0.709417\pi$
$881$	−36.2982	−1.22292	−0.611458	+	0.791277i	$0.709417\pi$
$882$	18.8052	0.633205
$883$	−2.16204	−0.0727583	−0.0363791	−	0.999338i	$-0.511582\pi$
$883$	−2.16204	−0.0727583	−0.0363791	+	0.999338i	$0.511582\pi$
$884$	−16.0147	−0.538634
$885$	1.49840	0.0503681
$886$	−9.30859	−0.312728
$887$	36.5266	1.22644	0.613221	−	0.789911i	$-0.289873\pi$
$887$	36.5266	1.22644	0.613221	+	0.789911i	$0.289873\pi$
$888$	−2.93323	−0.0984327
$889$	−7.76796	−0.260529
$890$	−13.5212	−0.453232
$891$	5.38573	0.180429
$892$	3.36530	0.112678
$893$	11.1104	0.371796
$894$	−32.4474	−1.08520
$895$	30.7709	1.02856
$896$	7.58949	0.253547
$897$	19.8530	0.662872
$898$	38.6498	1.28976
$899$	−36.7823	−1.22676
$900$	2.80340	0.0934466
$901$	13.3605	0.445102
$902$	82.8760	2.75947
$903$	0	0
$904$	−4.86799	−0.161907
$905$	−24.8899	−0.827367
$906$	31.1893	1.03619
$907$	23.9117	0.793976	0.396988	−	0.917824i	$-0.370056\pi$
$907$	23.9117	0.793976	0.396988	+	0.917824i	$0.370056\pi$
$908$	−14.7764	−0.490372
$909$	−6.86902	−0.227831
$910$	−5.78091	−0.191635
$911$	−20.8468	−0.690685	−0.345343	−	0.938477i	$-0.612237\pi$
$911$	−20.8468	−0.690685	−0.345343	+	0.938477i	$0.612237\pi$
$912$	−15.6711	−0.518922
$913$	−33.8669	−1.12083
$914$	−56.3018	−1.86230
$915$	−10.4261	−0.344676
$916$	−0.689788	−0.0227912
$917$	−6.40623	−0.211552
$918$	50.7966	1.67654
$919$	−26.0929	−0.860725	−0.430362	−	0.902656i	$-0.641614\pi$
$919$	−26.0929	−0.860725	−0.430362	+	0.902656i	$0.641614\pi$
$920$	17.6097	0.580575
$921$	−23.0428	−0.759287
$922$	−25.4751	−0.838978
$923$	−12.4438	−0.409592
$924$	−2.66174	−0.0875647
$925$	−2.54452	−0.0836633
$926$	31.0118	1.01911
$927$	−26.1803	−0.859875
$928$	46.4557	1.52498
$929$	10.3828	0.340648	0.170324	−	0.985388i	$-0.445519\pi$
$929$	10.3828	0.340648	0.170324	+	0.985388i	$0.445519\pi$
$930$	−12.9276	−0.423913
$931$	−18.0652	−0.592063
$932$	−23.1505	−0.758321
$933$	−6.81386	−0.223076
$934$	5.91695	0.193609
$935$	−42.4672	−1.38883
$936$	10.1726	0.332503
$937$	23.6950	0.774081	0.387040	−	0.922063i	$-0.373497\pi$
$937$	23.6950	0.774081	0.387040	+	0.922063i	$0.373497\pi$
$938$	−3.89132	−0.127056
$939$	24.2292	0.790689
$940$	−6.42420	−0.209534
$941$	−24.6205	−0.802607	−0.401303	−	0.915945i	$-0.631443\pi$
$941$	−24.6205	−0.802607	−0.401303	+	0.915945i	$0.631443\pi$
$942$	−12.9053	−0.420476
$943$	−59.4063	−1.93453
$944$	3.66698	0.119350
$945$	5.65218	0.183865
$946$	0	0
$947$	−6.75858	−0.219624	−0.109812	−	0.993952i	$-0.535025\pi$
$947$	−6.75858	−0.219624	−0.109812	+	0.993952i	$0.535025\pi$
$948$	13.7971	0.448108
$949$	−24.1766	−0.784805
$950$	−8.73663	−0.283454
$951$	25.1079	0.814181
$952$	6.21176	0.201324
$953$	49.8456	1.61466	0.807329	−	0.590101i	$-0.200912\pi$
$953$	49.8456	1.61466	0.807329	+	0.590101i	$0.200912\pi$
$954$	6.82147	0.220853
$955$	33.4170	1.08135
$956$	3.14211	0.101623
$957$	49.5337	1.60120
$958$	40.7863	1.31775
$959$	−4.77865	−0.154311
$960$	−4.00696	−0.129324
$961$	−17.0866	−0.551181
$962$	7.42159	0.239282
$963$	−0.0889946	−0.00286781
$964$	−17.3926	−0.560178
$965$	37.3630	1.20276
$966$	6.18962	0.199148
$967$	−22.6357	−0.727915	−0.363958	−	0.931416i	$-0.618575\pi$
$967$	−22.6357	−0.727915	−0.363958	+	0.931416i	$0.618575\pi$
$968$	−14.8677	−0.477867
$969$	−17.4096	−0.559277
$970$	−0.554589	−0.0178068
$971$	−59.9381	−1.92351	−0.961753	−	0.273920i	$-0.911680\pi$
$971$	−59.9381	−1.92351	−0.961753	+	0.273920i	$0.911680\pi$
$972$	13.1369	0.421367
$973$	13.0141	0.417212
$974$	−7.51567	−0.240818
$975$	−7.08539	−0.226914
$976$	−25.5154	−0.816727
$977$	−15.8508	−0.507113	−0.253556	−	0.967321i	$-0.581600\pi$
$977$	−15.8508	−0.507113	−0.253556	+	0.967321i	$0.581600\pi$
$978$	−24.9656	−0.798311
$979$	−19.5972	−0.626328
$980$	10.4456	0.333671
$981$	8.73591	0.278916
$982$	26.6225	0.849559
$983$	−26.4577	−0.843870	−0.421935	−	0.906626i	$-0.638649\pi$
$983$	−26.4577	−0.843870	−0.421935	+	0.906626i	$0.638649\pi$
$984$	24.4405	0.779135
$985$	−4.97763	−0.158600
$986$	92.9165	2.95906
$987$	2.80923	0.0894188
$988$	7.85489	0.249897
$989$	0	0
$990$	−21.6825	−0.689116
$991$	−19.5746	−0.621809	−0.310904	−	0.950441i	$-0.600632\pi$
$991$	−19.5746	−0.621809	−0.310904	+	0.950441i	$0.600632\pi$
$992$	−17.5725	−0.557927
$993$	−10.9612	−0.347842
$994$	−3.87962	−0.123054
$995$	0.0229073	0.000726211 0
$996$	8.02787	0.254373
$997$	18.0624	0.572041	0.286020	−	0.958224i	$-0.407667\pi$
$997$	18.0624	0.572041	0.286020	+	0.958224i	$0.407667\pi$
$998$	64.0356	2.02701
$999$	−7.25633	−0.229580

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.n.1.15		18
43.14	even	21		43.2.g.a.24.3	yes	36
43.40	even	21		43.2.g.a.9.3	✓	36
43.42	odd	2		1849.2.a.o.1.4		18
129.14	odd	42		387.2.y.c.325.1		36
129.83	odd	42		387.2.y.c.181.1		36
172.83	odd	42		688.2.bg.c.353.2		36
172.143	odd	42		688.2.bg.c.497.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.9.3	✓	36	43.40	even	21
43.2.g.a.24.3	yes	36	43.14	even	21
387.2.y.c.181.1		36	129.83	odd	42
387.2.y.c.325.1		36	129.14	odd	42
688.2.bg.c.353.2		36	172.83	odd	42
688.2.bg.c.497.2		36	172.143	odd	42
1849.2.a.n.1.15		18	1.1	even	1	trivial
1849.2.a.o.1.4		18	43.42	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+1.70036 q^{2} +1.15587 q^{3} +0.891224 q^{4} -1.76341 q^{5} +1.96539 q^{6} +0.594565 q^{7} -1.88532 q^{8} -1.66397 q^{9} +O(q^{10})\)	\(q+1.70036 q^{2} +1.15587 q^{3} +0.891224 q^{4} -1.76341 q^{5} +1.96539 q^{6} +0.594565 q^{7} -1.88532 q^{8} -1.66397 q^{9} -2.99843 q^{10} -4.34581 q^{11} +1.03014 q^{12} +3.24267 q^{13} +1.01098 q^{14} -2.03827 q^{15} -4.98817 q^{16} -5.54154 q^{17} -2.82935 q^{18} +2.71801 q^{19} -1.57159 q^{20} +0.687239 q^{21} -7.38944 q^{22} +5.29682 q^{23} -2.17918 q^{24} -1.89039 q^{25} +5.51371 q^{26} -5.39093 q^{27} +0.529891 q^{28} -9.86102 q^{29} -3.46578 q^{30} +3.73006 q^{31} -4.71104 q^{32} -5.02318 q^{33} -9.42261 q^{34} -1.04846 q^{35} -1.48297 q^{36} +1.34602 q^{37} +4.62159 q^{38} +3.74810 q^{39} +3.32458 q^{40} -11.2155 q^{41} +1.16855 q^{42} -3.87309 q^{44} +2.93426 q^{45} +9.00650 q^{46} +4.08771 q^{47} -5.76566 q^{48} -6.64649 q^{49} -3.21435 q^{50} -6.40528 q^{51} +2.88995 q^{52} -2.41097 q^{53} -9.16652 q^{54} +7.66343 q^{55} -1.12095 q^{56} +3.14166 q^{57} -16.7673 q^{58} -0.735135 q^{59} -1.81655 q^{60} +5.11518 q^{61} +6.34245 q^{62} -0.989339 q^{63} +1.96587 q^{64} -5.71815 q^{65} -8.54121 q^{66} -3.84908 q^{67} -4.93875 q^{68} +6.12242 q^{69} -1.78276 q^{70} -3.83751 q^{71} +3.13711 q^{72} -7.45576 q^{73} +2.28873 q^{74} -2.18505 q^{75} +2.42235 q^{76} -2.58387 q^{77} +6.37312 q^{78} +13.3934 q^{79} +8.79617 q^{80} -1.23929 q^{81} -19.0703 q^{82} +7.79301 q^{83} +0.612483 q^{84} +9.77199 q^{85} -11.3980 q^{87} +8.19324 q^{88} +4.50944 q^{89} +4.98929 q^{90} +1.92798 q^{91} +4.72065 q^{92} +4.31146 q^{93} +6.95057 q^{94} -4.79295 q^{95} -5.44534 q^{96} +0.184960 q^{97} -11.3014 q^{98} +7.23130 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} - 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} - 25 q^{18} - 31 q^{19} - 25 q^{20} - 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} - 27 q^{26} - 23 q^{27} - 20 q^{28} - 37 q^{29} + 17 q^{30} - 12 q^{31} - 39 q^{32} - 38 q^{33} - 14 q^{34} + 16 q^{35} + 47 q^{36} + 19 q^{37} + 56 q^{38} - 46 q^{39} + 6 q^{40} - 7 q^{41} + q^{42} + 7 q^{44} - 23 q^{45} + 47 q^{46} - q^{47} - 15 q^{48} - 6 q^{49} + 3 q^{50} - 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} - 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} - 28 q^{61} - 33 q^{62} - 26 q^{63} + 10 q^{64} - 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} - 7 q^{69} + 34 q^{70} - 86 q^{71} + 2 q^{72} + 27 q^{73} - 79 q^{74} - 31 q^{75} - 59 q^{76} - 43 q^{77} + 91 q^{78} + 17 q^{79} - 8 q^{80} - 10 q^{81} - 13 q^{82} - 12 q^{83} - 32 q^{84} - 28 q^{85} - 43 q^{87} + 23 q^{88} - 51 q^{89} + 10 q^{90} + 20 q^{91} + 18 q^{92} + 30 q^{93} + 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} + 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 - 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 - 25 * q^18 - 31 * q^19 - 25 * q^20 - 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 - 27 * q^26 - 23 * q^27 - 20 * q^28 - 37 * q^29 + 17 * q^30 - 12 * q^31 - 39 * q^32 - 38 * q^33 - 14 * q^34 + 16 * q^35 + 47 * q^36 + 19 * q^37 + 56 * q^38 - 46 * q^39 + 6 * q^40 - 7 * q^41 + q^42 + 7 * q^44 - 23 * q^45 + 47 * q^46 - q^47 - 15 * q^48 - 6 * q^49 + 3 * q^50 - 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 - 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 - 28 * q^61 - 33 * q^62 - 26 * q^63 + 10 * q^64 - 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 - 7 * q^69 + 34 * q^70 - 86 * q^71 + 2 * q^72 + 27 * q^73 - 79 * q^74 - 31 * q^75 - 59 * q^76 - 43 * q^77 + 91 * q^78 + 17 * q^79 - 8 * q^80 - 10 * q^81 - 13 * q^82 - 12 * q^83 - 32 * q^84 - 28 * q^85 - 43 * q^87 + 23 * q^88 - 51 * q^89 + 10 * q^90 + 20 * q^91 + 18 * q^92 + 30 * q^93 + 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 + 5 * q^98 + 38 * q^99

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